A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be n(n2+1)/2? Are there any other hidden properties of a…
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How much force can a rubber band withstand before breaking? Do rubber bands that stretch longer take more or less force to break? How does the elasticity of a rubber band change with temperature? Use a spring scale to measure the applied force, and a meter stick or ruler to measure the change in length. Recording with a video camera (or possibly two) can help you to capture the values at the moment before the rubber band breaks. You can change the temperature of the rubber bands using…
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The Falkirk Wheel is a rotating boat lift connecting the Forth and Clyde Canal with the Union Canal near Falkirk in central Scotland. It consists of two diametrically opposed caissons which rotate to lift boats between the two canals through a height of 35 meters. The wheel is always perfectly balanced and, despite its enormous mass, rotates through 180° in less than four minutes, using just 1.5 kilowatt-hours (Wikipedia contributors, 2006). Do background…
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If you like to fish and you'd rather not be telling the story of "the one that got away," then this is a project for you. What combination of properties makes for the best fishing line? Here are some suggestions for getting started on your background research into fishing line properties: knot strength, abrasion strength, shock strength, tensile strength, limpness, controlled stretch, and desired range of visibility (Dodson, 2006). Choose the properties that you think are most important, and…
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How do you turn a 2-dimensional piece of paper into a 3-dimensional work of art? Origami, the classical art of Japanese paper folding, is loaded with mathematical themes and concepts. What are the common folds in origami, and how do they combine to create 3-dimensional structure? Can you classify different types of origami into classes based upon the types of folds they use? Can you show Kawasaki's Theorem, that if you add up the angle measurements of every other angle around a point, the sum…
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You can measure the diameter of the Sun (and Moon) with a pinhole and a ruler! All you need to know is some simple geometry and the average distance between the Earth and Sun (or Moon). An easy way to make a pinhole is to cut a square hole (2-3 cm across) in the center of a piece of cardboard. Carefully tape a piece of aluminum foil flat over the hole. Use a sharp pin or needle to poke a tiny hole in the center of the foil. Use the pinhole to project an image of the Sun onto a wall or piece…
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You can investigate how the geography of an area makes it prone to severe flash floods. Some areas, typically gullies or canyons, can flood extremely rapidly making it impossible to escape a flash flood. Compare the topography, or geographical shape, or these areas. What makes them prone to flash floods? Can you do an experiment showing how the flow of water increases as a channel narrows? Can you use topological maps of your region to identify areas at risk for flash floods? (NCAR, 2006;…
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You may know Lewis Carroll as the author of Alice in Wonderland, but did you know that in real life he was a mathematician who studied symbolic logic and logical reasoning? How can math help you solve Lewis Carroll's Logic Game? (Bogomolny, 2006) How are algorithms for solving the game Sudoku similar to solving a logic problem? (Hayes, 2006) For the super-advanced mathematical genius, try to evaluate currently available, logic-based computational tools, or design a better one!…
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Did you know that commercial airline pilots use high-tech flight simulators to learn how to fly big jumbo jets? Before they ever step behind the controls of a real jet they've already logged thousands of virtual air miles. It might not qualify you to fly a real jumbo jet, but you, too, can learn the logistics of aviation by experimenting with the types of flight simulators sold at computer game retailers. Use a flight simulator to investigate the relationship between flap settings and the stall…
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Some sequences of RNA can catalyze biochemical reactions, much like protein enzymes. These catalytic RNA sequences are called ribozymes. The function of a ribozyme depends upon the primary sequence of the RNA which folds into a 3-D structure. How do different ribozyme sequences fold? You can search for ribozyme sequences using Entrez BLAST (NCBI, 2006). Then you can use a program like MFOLD () to submit your sequence for an analysis of its predicted 3-D structures based upon thermodynamics…
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BioChem_p023

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Time Required

Very Long (1+ months)

Prerequisites

Advanced biology course, or willingness to read up on such topics extensively.

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